Phi and An Elegant Equation
Let me clarify. I was on vacation 20 years ago when I discovered an interesting and, in my opinion, elegant mathematical equation involving Phi.
Life intervened and 20 years later, while perusing one of my personal journals in which I keep math and physics thoughts, I stumbled upon the equation.
So I sat down and wrote a proof.
As far as I know it is original. I have researched and not found this published anywhere.
Note: This is not a story about Phi or the Golden Ratio. More on Phi and its relation to the Golden Ratio can be found here.
It is an equation I discovered, and the proof I subsequently wrote. The elegance of this equation has stuck in my mind for 20 years and I’d like to share with you.
Equation and Proof
As stated at GoldenNumber.Net,
Phi ( Φ = 1.618033988749895… ), most often pronounced fi like “fly,” is simply an irrational number like pi ( p = 3.14159265358979… ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation
Phi has many interesting properties and this appears to be another. I have tried something similar Things with PI, e and other irrational and transcendental numbers, but have not been successful in deriving any special equations. I find this an elegant little equation and will be experimenting with it further.
Thanks for reading!